Reduced Dimension Rovibrational Variational Calculations of the S 1 State of C 2 H 2 P. Bryan Changala, Joshua H. Baraban, Robert W. Field, John F. Stanton, and Anthony J. Merer 1

Overview Ab initio rovibrational treatment of S 1 C 2 H 2 – cis-trans isomerization & K-staggering Experimental observations of K-staggering Extending measurements with high resolution REMPI and hot band-enhanced spectra 2

Reduced dimension coordinates H1H1 H2H2 C2C2 C1C1 H1H1 H2H2 2 CCH bend angles 1 torsional angle 1 stretch (r CC ) 4 dimensions (+ 3 rotations) Span:s ν 2 (r CC stretch) ν 3 (sym. in-plane bend) ν 4 (torsion) ν 6 (asym. in-plane bend) + 3

Reduced dimension coordinates H1H1 H2H2 C2C2 C1C1 H1H1 H2H2 2 CCH bend angles 1 torsional angle 1 stretch (r CC ) 4 dimensions (+ 3 rotations) Span:s ν 2 (r CC stretch) ν 3 (sym. in-plane bend) ν 4 (torsion) ν 6 (asym. in-plane bend) + 3 Form bending polyads, B n

Reduced dimension coordinates H1H1 H2H2 C2C2 C1C1 H1H1 H2H2 2 CCH bend angles 1 torsional angle 1 stretch (r CC ) 4 dimensions (+ 3 rotations) Span:s ν 2 (r CC stretch) ν 3 (sym. in-plane bend) ν 4 (torsion) ν 6 (asym. in-plane bend) + 3

Methodological details 4D surface calculated at EOM-CCSDT/ANO1 level of theory Multi-valued internal coordinates treated with extended C omplete N uclear P ermutation I nversion methods Hougen & Merer, JMS, 267, 200 (2011); Hougen, JMS, 278, 41 (2012) Constrained 4D kinetic energy operator Two step basis set contraction scheme: (4+3)D bending- torsion-rotation- stretch (3+3)D bending- torsion-rotation 1D stretch 4

S 1 vibrational manifold E (cm -1 ) ν 2 (CC stretch) & ν 3 (trans bend) combinations and overtones: simple structure residual = < 1 cm -1 for ν cm -1 for ν 3 (2%) (overestimation of ω 3 )

S 1 vibrational manifold E (cm -1 ) ν 4 (torsion) & ν 6 (cis bend) fundamentals (nearly degenerate) residual = -16 cm -1 for ν cm -1 for ν 6 (3D calc. with finer PES within 1 cm -1 )

S 1 vibrational manifold E (cm -1 ) ν 4, ν 6 overtones group into polyads (resonant anharmonic interactions and Coriolis coupling)

S 1 vibrational manifold E (cm -1 ) B4B4 ν 4, ν 6 overtones group into polyads (resonant anharmonic interactions and Coriolis coupling)

Bending polyad structure 7 Ex. K=0-2 span 400 cm -1 ϵ rms = 4.9 cm -1 E-E 0 (cm -1 ) Variational predictions: Polyad structure robustly determined Residuals comparable to H eff models

Bending polyad structure 7 Ex. Q4Q4 Q6Q6 Q4Q4 Q6Q6 Q4Q4 Q6Q6 Q4Q4 Q6Q6 Q4Q4 Q6Q6 Polyad wavefunctions (3D)

Bending polyad structure 7 Ex. Q4Q4 Q6Q6 Q4Q4 Q6Q6 Q4Q4 Q6Q6 Q4Q4 Q6Q6 Q4Q4 Q6Q6 Effective vibrational angular momentum Polyad wavefunctions (3D)

S 1 vibrational manifold 8 cis levels E (cm -1 ) Stretch-bend combinations (E cal - E cal, cis v= 0 ) + E exp, cis v= 0

K-staggerings in cis and trans levels 9 cis stateObs (cm -1 )Calc ± v = (3) trans stateObs (cm -1 )Calc 3434 (0) * (-64*) *3D Minimally, need K = 0-2 measurements (for even/odd staggering) Ideally, want K = 0-4 (torsional staggering?, perturbations)

H atom action REMPI H atom REMPI LIF R Q P

(approximate) selection rule requires vibrationally excited (S 0 ) state levels to reach high aaa levels of the (S 1 ) state, eg: Hot band schemes 11 UV IR (gerade)(ungerade) vibrational excitation in hyperthermal pyrolysis nozzle (300 –1800 K)

Thermal population enhancement 12 crude temperature model:

Hot band IR-UV double resonance 13

Summary Understanding cis-trans in isomerization C 2 H 2 requires parallel quantum chemical and local empirical fit approaches Ab initio energy structure increasingly necessary as polyad patterns break down for isomerizing levels Ongoing efforts to measure higher K-structure – High resolution REMPI spectra – Hot band-enhanced spectra 14

Acknowledgements Collaborators: Prof. J. F. Stanton (UT-Austin) Prof. A. J. Merer (UBC/IAMS) Dr. J. T. Hougen (NIST) B. Broderick (WSU) Prof. A. Suits (WSU) Funding DOE Field Group Members: Julia Berk Jun Jiang Peter Richter Barratt Park 15

Pyrolysis Nozzle Zhang, et al. Rev. Sci. Instrum. 74, 3077 (2003) SiC Nozzle,aa Thermal bath Crude dissipation model: 10% C 2 H 2 in He (60 psi backing) S1

10 2 distinct differential operators. Uncomfortably large amount of algebra to derive analytic expressions Challenges of rovibrational variational calculations S2 is complicated Cartesian coordinates Internal coordinates

Benchmarking accuracy of vibrational fundamentals S3 for the frozen CH bonds

Benchmarking accuracy of vibrational fundamentals S4 *VPT2 calculations [Baraban, et al, Mol. Phys. 110, 2725 (2012)]

Dye Laser FL2002 WEX- LiNbO 3 PAC nm IR UV: nm, 100 µJ, 0.03 cm -1 IR: µm, 2 mJ, 0.15 cm Hz duty cycle Pulsed General Valve and Diffusion Pump Nd:YAG Dye Laser FL3002E BBO Te blue UV LIF Julia Berk REMPI S5